Statistical Learning TheoryProf. Giuseppe De Nicolao

Course Material

• Hastie&Tibshirani’s Slideshttps://www.r-bloggers.com/in-depth-introduction-to-machine-learning-in-15-hours-of-expert-videos/

• Textbook (basic)http://faculty.marshall.usc.edu/gareth-james/ISL/

• Textbook (advanced)https://web.stanford.edu/~hastie/ElemStatLearn//download.html

Books: basic

Books: advanced

Exam

• Written exam• 2 questions about theory (definitions, methods, proofs, ...)• 2 problems

• In addition, there might be• Mini-projects• Contests(1-3 points each)

Contents (1/2)• Introduction: Supervised and Unsupervised Learning.

• Statistical Learning: Statistical Learning and Regression, Curse of Dimensionality and Parametric Models, Assessing Model Accuracy and Bias-Variance Trade-off, Classification Problems and K-Nearest Neighbors.

• Linear Regression: Simple Linear Regression and Confidence Intervals, Hypothesis Testing, Multiple Linear Regression, Model Selection, Interactions and Nonlinearity.

• Classification: Introduction to Classification, Logistic Regression and Maximum Likelihood, Linear Discriminant Analysis and Bayes Theorem, Naive Bayes.

• Resampling Methods: Estimating Prediction Error and Validation Set Approach, K-fold Cross-Validation, Cross-Validation: The Right and Wrong Ways, The Bootstrap.

• Linear Model Selection and Regularization: Linear Model Selection and Best Subset Selection, Stepwise Selection, Estimating Test Error Using Mallow’s Cp, AIC, BIC, Adjusted R-squared, Cross-Validation, Shrinkage Methods and Ridge Regression, The Lasso, Principal Components Regression and Partial Least Squares.

Contents (2/2)

• Moving Beyond Linearity: Polynomial Regression, Piecewise Polynomials and Splines, Smoothing Splines, Local Regression and Generalized Additive Models.

• Tree-Based Methods: Decision Trees, Classification Trees and Comparison with Linear Models, Bootstrap Aggregation (Bagging) and Random Forests, Boosting.

• Support Vector Machines: Support Vector Classifier, Kernels and Support Vector Machines.• Unsupervised Learning: Unsupervised Learning and Principal Components Analysis, K-means

Clustering.

• The fallacies of learning: regression to mediocrity, the covariate shift, statistical significance vs practical significance, correlation is not causation, observational vs experimental studies.

The blog: https://statisticallearningtheory.wordpress.com/

Links to books, slides, video, etc

The Facebook page

Statistical learning

• Supervised statistical learning: building a statistical model for predicting, or estimating, an output based on one or more inputs.

• Unsupervised statistical learning: there are inputs but no supervising output; nevertheless we can learn relationships and structure from such data.